From 17c73a280f1dc64310c4f91357b5f40c00efea50 Mon Sep 17 00:00:00 2001
From: shirleymaza <166472849+shirleymaza@users.noreply.github.com>
Date: Fri, 14 Feb 2025 01:07:20 -0500
Subject: [PATCH] Added Bead Sort Algorithm #920

---
 algorithms/sort/bead_sort.py | 26 ++++++++++++++++++++++++++
 1 file changed, 26 insertions(+)
 create mode 100644 algorithms/sort/bead_sort.py

diff --git a/algorithms/sort/bead_sort.py b/algorithms/sort/bead_sort.py
new file mode 100644
index 000000000..0d949fa82
--- /dev/null
+++ b/algorithms/sort/bead_sort.py
@@ -0,0 +1,26 @@
+"""
+Bead Sort (also known as Gravity Sort) is a natural sorting algorithm that simulates how beads would settle under gravity on an abacus. It is most useful for sorting positive integers, especially when the range of numbers isn't excessively large. However, it is not a comparison-based sort and is generally impractical for large inputs due to its reliance on physical modeling.
+Time Complexity
+- Best Case: O(n) if the numbers are already sorted
+- Average Case: O(n^2) because each bead needs to be placed and then fall under gravity
+- Worst Case: O(n^2) since each bead must "fall" individually
+"""
+
+def bead_sort(arr):
+    if any(num < 0 for num in arr):
+        raise ValueError("Bead sort only works with non-negative integers.")
+
+    max_num = max(arr) if arr else 0
+    grid = [[0] * len(arr) for _ in range(max_num)]
+
+    # Drop beads (place beads in columns)
+    for col, num in enumerate(arr):
+        for row in range(num):
+            grid[row][col] = 1
+
+    # Let the beads "fall" (count beads in each row)
+    for row in grid:
+        sum_beads = sum(row)
+        for col in range(len(arr)):
+            row[col] = 1 if col < sum_beads else 0
+